Identifying risks in temporal supernetworks: an IO-SuperPageRank algorithm

Abstract

Complex systems pose risks characterized by factors such as uncertainty, nonlinearity, and diversity, making traditional risk measurement methods based on a probabilistic framework inadequate. Supernetworks can effectively model complex systems, and temporal supernetworks can capture the dynamic evolution of these systems. From the perspective of network stability, supernetworks can aid in risk identification for complex systems. In this paper, an IO-SuperPageRank algorithm is proposed based on the supernetwork topological structure. This algorithm reveals network instability by calculating changes in node importance, thereby helping to identify risks in complex systems. To validate the effectiveness of this algorithm, a four-layer supernetwork composed of scale-free networks is constructed. Simulated experiments are conducted to assess the impact of changes in intralayer edge numbers, intralayer node numbers, and interlayer superedge numbers on the risk indicator IO value. Linear regression and multiple tests were used to validate these relationships. The experiments show that changes in the three network topological indicators all bring about risks, with changes in intralayer node numbers having the most significant correlation with the risk indicator IO value. Compared to traditional measures of network node centrality and connectivity, this algorithm can more accurately predict the impact of node updates on network stability. Additionally, this paper collected trade data for crude oil, chemical light oil, man-made filaments and man-made staple fibers from the UN Comtrade Database. We constructed a man-made filaments and fibers supply chain temporal supernetwork, utilizing the algorithm to identify supply chain risks from December 2020 to October 2023. The study revealed that the algorithm effectively identified risks brought about by changes in international situations such as the Russia-Ukraine war, Israel–Hamas conflict, and the COVID-19 pandemic. This demonstrated the algorithm’s effectiveness in empirical analysis. In the future, we plan to further expand its application based on different scenarios, assess risks by analyzing changes in specific system elements, and implement effective risk intervention measures.